{ "model": { "rank": 6656, "code": "thing-q3884033", "model_id": "vr.tr.mathematical-operation", "name": "mathematical operation", "purpose": "Let an agent handle mathematical operations by arity, domain, properties and notation, and apply them correctly.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QLT", "industry": "", "version": "", "url": "/models/thing/q3884033/", "tier": 2, "score": 59, "payload": { "layer": "wikidata", "aliases": [ "cancelling out", "cross-canceling", "transclusion", "self-mapping", "clamping", "unary function", "string operation", "graph operation", "Micro-operation", "polygonalization", "direct sum of modules", "arithmetic operation", "wavelet extraction", "weighted sum", "direct sum", "ternary operation", "hyperoperation", "internal operation", "Euclidean space transformation", "knot operation", "polytope operation", "morphological operation", "set operation", "pushforward", "Left Factorial", "classical operation", "semidirect product", "circular shift", "left factoring", "closure of a relation", "operation on data structure", "algebraic operation", "nullary operation", "relational algebra operation", "blowing down", "extension and contraction of ideals", "function application", "vector multiplication", "iterated binary operation", "join and meet" ], "aliasCount": 73, "merged": 73, "knownIn": 59, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": null, "source": { "dataset": "wikidata", "item": "Q3884033", "url": "https://www.wikidata.org/wiki/Q3884033", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-11T08:54:20Z", "providers": [ "Claude" ], "breadth": "written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify", "pass": 2, "wave": 1, "engine": "claude" }, "metaModel": { "id": "THING-Q3884033", "registryId": "vr.tr.mathematical-operation", "name": "mathematical operation", "version": "0.2.0-wave.1", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QLT" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q3884033/", "model": { "registry_id": "vr.tr.mathematical-operation", "name": "mathematical operation", "purpose": "Let an agent handle mathematical operations by arity, domain, properties and notation, and apply them correctly.", "definition": "A function or rule that takes one or more inputs (operands) and produces an output, such as addition, multiplication, negation, composition, clamping or cancelling; operations may be unary, binary or n-ary.", "what_it_is_for": "Building calculations, algebraic structures and algorithms.", "affordances": [ "identify the operation and its arity", "check properties such as associativity", "apply order of operations", "implement operations in code" ], "distinguishing_features": [ "Maps inputs to output", "Has arity and domain", "Properties define structures", "Precedence rules in notation" ], "appearance": "Symbols such as +, x, -, composition and function notation.", "visual_identification": [ "Unary, binary or n-ary", "Notation and precedence", "Operations in computing such as clamping" ], "physical_properties": [], "families_and_kinds": [ "arithmetic operations", "unary operations such as negation", "binary operations", "set and logical operations", "function composition" ], "related_models": [ { "relation": "is a kind of", "target": "function", "why": "category" }, { "relation": "includes", "target": "addition", "why": "example" }, { "relation": "defines", "target": "algebraic structure", "why": "structure" }, { "relation": "is implemented in", "target": "algorithm", "why": "computing" } ], "identifiers": [], "standards_and_regulation": [ "ISO 80000-2 notation", "IEEE 754 floating-point operations" ], "failure_modes_and_hazards": [ "Precedence errors", "Operations undefined on some inputs", "Floating-point surprises" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "operation", "name": "Operation", "description": "Which operation.", "rationale": "Arity and domain.", "layers": [ { "id": "arity", "name": "Arity", "description": "Number of inputs.", "findings": [ { "id": "arity-finding", "name": "Arity", "description": "Arity.", "questions": [ { "text": "How many operands does it take?", "kind": "definition" }, { "text": "On which set is it defined?", "kind": "definition" } ] } ] }, { "id": "notation", "name": "Notation", "description": "Symbols.", "findings": [ { "id": "notation-finding", "name": "Notation", "description": "Notation.", "questions": [ { "text": "How is it written?", "kind": "definition" }, { "text": "What precedence does it have?", "kind": "definition" } ] } ] } ] }, { "id": "properties", "name": "Properties", "description": "Laws.", "rationale": "Properties enable reasoning.", "layers": [ { "id": "laws", "name": "Laws", "description": "Associativity and more.", "findings": [ { "id": "laws-finding", "name": "Laws", "description": "Algebraic laws.", "questions": [ { "text": "Is it associative, commutative or distributive?", "kind": "boundary" }, { "text": "Does it have an identity or inverse?", "kind": "boundary" } ] } ] }, { "id": "closure", "name": "Closure", "description": "Staying in the set.", "findings": [ { "id": "closure-finding", "name": "Closure", "description": "Closure.", "questions": [ { "text": "Is the set closed under the operation?", "kind": "boundary" }, { "text": "Where is it undefined?", "kind": "boundary" } ] } ] } ] }, { "id": "computing", "name": "Computing", "description": "Implementation.", "rationale": "Code implements operations.", "layers": [ { "id": "implementation", "name": "Implementation", "description": "Code.", "findings": [ { "id": "implementation-finding", "name": "Implementation", "description": "Implementation.", "questions": [ { "text": "How is the operation implemented in code?", "kind": "action" }, { "text": "Are edge cases handled?", "kind": "boundary" } ] } ] }, { "id": "precision", "name": "Precision", "description": "Floating point.", "findings": [ { "id": "precision-finding", "name": "Precision", "description": "Precision.", "questions": [ { "text": "Could rounding change the result?", "kind": "boundary" }, { "text": "Is exact arithmetic needed?", "kind": "action" } ] } ] } ] }, { "id": "learning", "name": "Learning", "description": "Teaching.", "rationale": "Order of operations confuses.", "layers": [ { "id": "order", "name": "Order", "description": "Precedence.", "findings": [ { "id": "order-finding", "name": "Order", "description": "Order of operations.", "questions": [ { "text": "What result does the order of operations give here?", "kind": "measurement" }, { "text": "Would brackets make it clearer?", "kind": "action" } ] } ] }, { "id": "examples", "name": "Examples", "description": "Illustrations.", "findings": [ { "id": "examples-finding", "name": "Examples", "description": "Examples.", "questions": [ { "text": "Which examples illustrate the operation?", "kind": "action" }, { "text": "What misconceptions are common?", "kind": "boundary" } ] } ] } ] } ] }, "openQuestions": [ "Should operation classes be separate entries?", "How should notation conventions be recorded?", "How should computing operations be linked?" ], "statistics": { "bundles": 4, "layers": 8, "findings": 8, "questions": 16 } }, "draft": { "generator": "vr.draft.v3", "status": "draft-generated", "researched": false, "archetype": "abstract concept", "method": "Written from the archetype playbook - what this kind of thing needs beyond identity and provenance - and from the structure that recurred across 6,333 models already researched by two engines. Applied to this entry by rule. No source was read for this thing and no claim here is researched. This entry carries no facets of its own, so they were inferred from its domain - a guess about a whole domain applied to one thing.", "facetsInferred": true, "nextPass": "A researcher replaces this draft with a sourced specification. Treat every sentence below as a proposal to argue with.", "purpose": "Give an agent a durable, checkable way to recognise a mathematical operation, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent handle mathematical operations by arity, domain, properties and notation, and apply them correctly.", "characteristics": { "substance": "abstract", "origin": "conceptual", "agency": "inert" }, "whatYouCanDoWithIt": [ "observed and measured" ], "distinguishingFeatures": [ "Names folded into this entry, which a task may need to split apart again: cancelling out, cross-canceling, transclusion, self-mapping, clamping, unary function, string operation, graph operation, Micro-operation, polygonalization, direct sum of modules, arithmetic operation.", "73 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 59 Wikipedia languages, which is a measure of how widely the thing is known, not of how important it is." ], "openQuestionsForResearch": [ "Which of the bundles below does a real task actually need, and which are ceremony?", "What does this thing have that the facets do not capture at all?", "Which neighbouring kind is most often confused with a mathematical operation, and on what evidence are they told apart?" ], "whatItIsMadeOf": "an abstraction with no physical instance", "physicalCharacter": [ "Does nothing on its own; everything it does, something else did to it.", "These come from the domain this entry sits in rather than from the entry itself, so treat them as a first guess about the whole domain applied to one thing." ], "whatCanBeDoneWithIt": [ "observe it, measure it, record its state" ], "howItIsRecognised": [ "Nothing to see. What is recognised is an instance of it, and which instances count is exactly what is argued about." ], "relatedModels": [ { "relation": "covers", "note": "Finer kinds folded into this entry because telling them apart needs a task that asks for it. Each is a model waiting to be split out when one does.", "targets": [ "cancelling out", "cross-canceling", "transclusion", "self-mapping", "clamping", "unary function", "string operation", "graph operation", "Micro-operation", "polygonalization", "direct sum of modules", "arithmetic operation" ] } ], "standing": "Described in 59 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 73 finer distinctions are held inside this entry as names rather than as separate models.", "structure": { "bundles": [ { "id": "identity-and-classification", "name": "Identity, naming and classification", "description": "How an agent tells one mathematical operation from another, and a mathematical operation from things that resemble it.", "rationale": "Recognition comes before every other claim. Without stable identity nothing else in the model can be trusted to be about the same thing twice.", "layers": [ { "id": "naming-and-identifiers", "name": "Names and identifiers", "description": "The names this thing goes by and the identifiers that survive translation and time.", "findings": [ { "id": "preferred-name-and-aliases", "name": "Preferred name, aliases and local names", "description": "Which name to use, which names mean the same thing, and which merely sound similar.", "questions": [ { "id": "preferred-name-and-aliases-q01", "text": "What identifies and describes the name of a mathematical operation, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "preferred-name-and-aliases-q02", "text": "Who or what asserted this about the name of a mathematical operation, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "preferred-name-and-aliases-q03", "text": "What may an agent decide or do once the name of a mathematical operation is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] }, { "id": "stable-identifiers", "name": "Stable identifiers and external keys", "description": "Identifiers that keep pointing at this kind of thing across systems and languages.", "questions": [ { "id": "stable-identifiers-q01", "text": "What identifies and describes an identifier for a mathematical operation, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "stable-identifiers-q02", "text": "Who or what asserted this about an identifier for a mathematical operation, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "stable-identifiers-q03", "text": "What may an agent decide or do once an identifier for a mathematical operation is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] }, { "id": "classification-and-granularity", "name": "Classification and granularity", "description": "Where a mathematical operation sits among kinds, and how finely a task needs to cut it.", "findings": [ { "id": "kind-and-parents", "name": "Kind, parents and neighbouring kinds", "description": "The classes this thing belongs to and the ones it is next to.", "questions": [ { "id": "kind-and-parents-q01", "text": "What identifies and describes the kind of a mathematical operation, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "kind-and-parents-q02", "text": "Who or what asserted this about the kind of a mathematical operation, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "kind-and-parents-q03", "text": "What may an agent decide or do once the kind of a mathematical operation is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] }, { "id": "distinguishing-features", "name": "Distinguishing features", "description": "What separates a mathematical operation from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a mathematical operation, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "distinguishing-features-q02", "text": "Who or what asserted this about what distinguishes a mathematical operation, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "distinguishing-features-q03", "text": "What may an agent decide or do once what distinguishes a mathematical operation is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] } ] }, { "id": "state-and-lifecycle", "name": "State and lifecycle", "description": "The states a mathematical operation passes through and the events that move it between them.", "rationale": "Most decisions about a thing depend on what state it is in now, which is a claim with a time on it, not a property.", "layers": [ { "id": "lifecycle-stages", "name": "Lifecycle stages", "description": "From coming into existence to ceasing to be one of these.", "findings": [ { "id": "stages-and-transitions", "name": "Stages and transitions", "description": "The stages worth naming and what moves a mathematical operation between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a mathematical operation, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "stages-and-transitions-q02", "text": "Who or what asserted this about the lifecycle of a mathematical operation, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "stages-and-transitions-q03", "text": "What may an agent decide or do once the lifecycle of a mathematical operation is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] }, { "id": "observations-and-status", "name": "Observations and current status", "description": "What is observed about a mathematical operation, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a mathematical operation is recorded so that it can be superseded rather than overwritten.", "questions": [ { "id": "observation-record-q01", "text": "What identifies and describes an observation of a mathematical operation, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "observation-record-q02", "text": "Who or what asserted this about an observation of a mathematical operation, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "observation-record-q03", "text": "What may an agent decide or do once an observation of a mathematical operation is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] } ] }, { "id": "definitions-in-contest", "name": "Definitions and who holds them", "description": "What mathematical operation is taken to mean, and by whom.", "rationale": "When a field disagrees about a concept, the disagreement is the content. A model that picks one definition silently destroys the information.", "layers": [ { "id": "competing-definitions", "name": "Competing definitions", "description": "The main readings and the traditions behind them.", "findings": [ { "id": "definition-map", "name": "Definitions and their holders", "description": "Each definition with the school or body that holds it.", "questions": [ { "id": "definition-map-q01", "text": "Which definitions of mathematical operation are in use, and which tradition or body holds each?", "kind": "definition" }, { "id": "definition-map-q02", "text": "What turns on the difference between them in practice?", "kind": "boundary" } ] } ] }, { "id": "operationalisation", "name": "Operationalisation", "description": "How it is measured or applied when it has to be.", "findings": [ { "id": "operational-record", "name": "Measures and proxies", "description": "Instruments and indicators used to stand in for it.", "questions": [ { "id": "operational-record-q01", "text": "How is mathematical operation operationalised or measured in practice, and by what instrument?", "kind": "measurement" }, { "id": "operational-record-q02", "text": "What does that operationalisation leave out, and when does that matter?", "kind": "boundary" } ] } ] } ] }, { "id": "instances-and-use", "name": "Instances, use and consequence", "description": "What counts as an instance of mathematical operation and what follows from calling something that.", "rationale": "Applying a concept is an act with consequences, so a model must say what the label licenses and what it does not.", "layers": [ { "id": "instances", "name": "What counts as an instance", "description": "Clear cases, borderline cases and non-cases.", "findings": [ { "id": "instance-tests", "name": "Tests for an instance", "description": "What would settle whether something falls under it.", "questions": [ { "id": "instance-tests-q01", "text": "What would settle whether something is an instance of mathematical operation?", "kind": "boundary" }, { "id": "instance-tests-q02", "text": "Which borderline cases are argued about, and on what grounds?", "kind": "definition" } ] } ] }, { "id": "consequence", "name": "Consequence of application", "description": "Rights, duties or decisions that follow from the label.", "findings": [ { "id": "consequence-record", "name": "What the label licenses", "description": "What an agent may do once something is classified this way.", "questions": [ { "id": "consequence-record-q01", "text": "What follows practically once something is treated as mathematical operation?", "kind": "action" }, { "id": "consequence-record-q02", "text": "What must an agent not infer from the label alone?", "kind": "action" } ] } ] } ] }, { "id": "provenance-and-evidence", "name": "Provenance, evidence and time", "description": "Where every claim about a mathematical operation came from and when it held.", "rationale": "A claim without a source and a time cannot be superseded, only overwritten, and an agent that overwrites loses the ability to explain itself.", "layers": [ { "id": "source-and-authority", "name": "Source and authority", "description": "Who said it, on what evidence, and how strongly.", "findings": [ { "id": "claim-provenance", "name": "Claim provenance and confidence", "description": "The authority behind each claim about a mathematical operation and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a mathematical operation, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "claim-provenance-q02", "text": "Who or what asserted this about a claim about a mathematical operation, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "claim-provenance-q03", "text": "What may an agent decide or do once a claim about a mathematical operation is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] }, { "id": "time-and-versions", "name": "Time, versions and supersession", "description": "When a claim was true, when it was learnt, and what replaced it.", "findings": [ { "id": "validity-and-supersession", "name": "Validity period and supersession", "description": "How an old claim about a mathematical operation is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a mathematical operation, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "validity-and-supersession-q02", "text": "Who or what asserted this about the validity of a claim about a mathematical operation, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "validity-and-supersession-q03", "text": "What may an agent decide or do once the validity of a claim about a mathematical operation is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] } ] } ] }, "statistics": { "bundles": 5, "layers": 10, "findings": 12, "questions": 32 } } } }